Sequential Experimental Design

As model reasoning gets cheaper, the physical experiment becomes the slow and costly step in discovery. Each experiment returns a noisy reading: a high value can mean a good candidate or a lucky draw. With a fixed budget, an AI agent must keep choosing between exploring a new candidate and confirming a promising one by re-testing it. We measure that choice in Wellocate, a simulated assay campaign with known true values. It is built on a generated landscape and on two real protein datasets, GB1 and PhoQ, scrambled so no model can answer from memory. We test five language models as minimal agents, with no tools and no memory beyond the history in each prompt. They misallocate in both directions. Three over-confirm, spending most of the budget re-testing. On the generated landscape one under-confirms, trusting single readings, and there every model ends with a worse final pick than a basic scripted strategy. Each failure has its own cause. The over-confirmers run short of new candidates worth trying: a list of untried candidates cuts their re-testing and, on real protein data, makes two of them pick much better. A running summary of their readings or a description of the landscape changes it by at most five percentage points. For the under-confirmer, re-testing its top candidates in a final round, replayed on its own campaigns, recovers only about a quarter of what it loses by picking the wrong candidate. This suggests confirmation has to run through the whole campaign. We release Wellocate as a benchmark and reinforcement-learning environment with frozen splits and scripted baselines. With it, anyone can measure how an agent splits its budget before trusting it with real experiments, and train agents to split it better. Code, data and the environment are available at https://github.com/Xstendyl/wellocate.

Generalist robot manipulation policies trained on large, diverse datasets have shown remarkable promise across a wide range of tasks. However, rigorously evaluating these policies remains a fundamental challenge. Real-world performance depends on a large combinatorial space of task factors including object poses and camera viewpoints, making full, exhaustive evaluation intractable. Additionally, real hardware evaluation is slow and resource-intensive, so current practice is to use narrow test suites that can miss critical failure modes and misrepresent true deployment readiness. We propose an active evaluation framework that addresses this challenge by treating policy evaluation as a sequential experimental design problem. Our approach fits a probabilistic surrogate model over a structured space of task factors and adaptively selects evaluation configurations to maximize information gain over the policy's performance distribution, allowing for sample-efficient characterization of policy behavior across unseen conditions and a systematic identification of failure-prone regions. We conduct 2331 real-world evaluations across 3 tasks with 3 factor variations and find that our approach typically saves the evaluator at least 20-40% of trials compared to typical random testing.

In X-ray tomography, reconstruction quality generally improves with larger numbers of projections. However, more projections increase experiment costs, acquisition time and the radiation dose imparted to the sample. One mitigation to these trade-offs is to adopt a sequential design of experiments, in which each subsequent measurement is determined as a function of previously acquired data in order to maximize information gain. In practice, a widely used heuristic to maximize information is to align beams with the edges of the sample. A key challenge, however, is that the true sample is unknown, so identifying edge-aligned beams typically requires reconstructing the sample based on available measurements. This work proposes a novel sequential design method that identifies edge-aligned measurements directly from the sinogram, bypassing any reconstruction, thereby improving computational efficiency and reducing the experimental design's susceptibility to reconstruction errors. Our method dynamically selects the next set of measurement beams by maximizing an acquisition function that balances exploration and exploitation over the domain of all possible measurements, improving reconstruction quality while reducing measurement redundancy.

High-throughput experimentation can evaluate many reaction conditions, yet combinatorial condition spaces still exceed the available experiment budget. This makes experiment selection a sequential decision problem: each new condition must be chosen from limited observations before its outcome is known. LLMs can express task-specific selection logic. A direct recommendation, however, is neither a persistent executable object that can be validated and revised nor an independently auditable decision rule. We introduce CARE, a reference-conditioned controller that separates program synthesis from experiment selection. An LLM writes an executable scoring program that ranks the remaining conditions, while a non-LLM reference policy supplies a numerical candidate and support summary. CARE forms an optional alternative from the program, applies a reference-conditioned intervention gate to compare it with the reference, and records the decision before the selected outcome is revealed. Each new outcome updates controller state and can trigger retention, revision, or regeneration of the active program. This outcome-guided program evolution changes the scoring logic without updating the LLM parameters. In matched offline replay with 30 seeds on eight reaction-optimization tasks, CARE attains the lowest normalized regret, the highest normalized best-so-far AUC, and the highest Top-1% Success@15 among the evaluated methods. These results support using a scoring program written by an LLM as one component of a reference-conditioned optimizer rather than as a standalone experiment selector.

This study presents an iterative AI-guided workflow that accelerates graphite-based anode development by improving both formulation feasibility and process robustness. Sequential learning via AI/ML-guided multiobjective inverse design for anode optimization was implemented using the Citrine Platform. Starting from a noisy, incomplete dataset, the Citrine Platform was used to generate early surrogate models, which despite low predictive certainty highlighted missing process constraints. By iteratively adding feasibility labels and boundary condition failures, the workflow rapidly converged toward manufacturable, higher-performing formulations. Fabrication reliability improved from frequent process failures to 100% successful cell production, while the fraction of cells delivering $\geq$ 350 mAh g$^{-1}$ increased from 28.4% to 84.8%, with capacity retention rising from 42.1% to 97.3%. These results demonstrate that structured, feedback-driven AI workflows can transform imperfect industrial data into actionable guidance, enabling faster, more reproducible optimization of battery electrode manufacturing.

Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget limitations, varying costs, or physical constraints that restrict how designs evolve over time. In this paper, we introduce a novel approach to BED that enables constrained optimization of experimental designs by combining offline pre-training of an amortized policy and a posterior network with online multi-step lookahead planning using scenario trees. We empirically demonstrate that our method yields substantially more informative design sequences than existing methods across a range of constrained BED tasks, while incurring only a modest additional computational overhead.

Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model misspecification and develop a unified framework that covers both contextual bandit and dynamic settings. Theoretically, we prove that our design bounds the worst-case mean squared error of the estimated treatment effect. Empirically, we demonstrate the effectiveness of the proposed approach using synthetic and real-world datasets from a leading technology company.

The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to optimize genetic circuits under both forms of uncertainty. By employing simulator models based on differential equations or Markov jump processes alongside a reinforcement learning (RL) policy-based approach, our method suggests experiments that adapt to unknown laboratory conditions while accounting for inherent stochasticity. While previous Bayesian methods address uncertainty through iterative experiment-inference-optimization cycles, they typically require computationally expensive inference and optimization steps after each experimental round, leading to delays. To overcome this bottleneck, we propose an amortized approach trained up-front across a distribution of possible uncertain parameters. This strategy sidesteps the need for explicit parameter inference during the design cycle, enabling immediate, observation-based adaptation. We demonstrate our framework on models for heterologous gene expression and a repressilator circuit, showing that it efficiently handles both molecular noise and cross-laboratory variability.

Regulatory approval of products in high-stakes domains such as drug development requires statistical evidence of safety and efficacy through large-scale randomized controlled trials. However, the high financial cost of these trials may deter developers who lack absolute certainty in their product's efficacy, ultimately stifling the development of `moonshot' products that could offer high social utility. To address this inefficiency, in this paper, we introduce a statistical protocol for experimentation where the product developer (the agent) conducts a randomized controlled trial sequentially and the regulator (the principal) partially subsidizes its cost. By modeling the protocol using a belief Markov decision process, we show that the agent's optimal strategy can be found efficiently using dynamic programming. Further, we show that the social utility is a piecewise linear and convex function over the subsidy level the principal selects, and thus the socially optimal subsidy can also be found efficiently using divide-and-conquer. Simulation experiments using publicly available data on antibiotic development and approval demonstrate that our statistical protocol can be used to increase social utility by more than 35$$\% relative to standard, non-sequential protocols.

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We then propose an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, our method consistently outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.

Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation. We propose ALMAB-DC, a GP-based sequential design framework combining active learning, multi-armed bandits (MAB), and distributed asynchronous computing for expensive black-box experimentation. A Gaussian process surrogate with uncertainty-aware acquisition identifies informative query points; a UCB or Thompson-sampling bandit controller allocates evaluations across parallel workers; and an asynchronous scheduler handles heterogeneous runtimes. We present cumulative regret bounds for the bandit components and characterize parallel scalability via Amdahl's Law. We validate ALMAB-DC on five benchmarks. On the two statistical experimental-design tasks, ALMAB-DC achieves lower simple regret than Equal Spacing, Random, and D-optimal designs in dose--response optimization, and in adaptive spatial field estimation matches the Greedy Max-Variance benchmark while outperforming Latin Hypercube Sampling; at $K=4$ the distributed setting reaches target performance in one-quarter of sequential wall-clock rounds. On three ML/engineering tasks (CIFAR-10 HPO, CFD drag minimization, MuJoCo RL), ALMAB-DC achieves 93.4% CIFAR-10 accuracy (outperforming BOHB by 1.7,pp and Optuna by 1.1,pp), reduces airfoil drag to $C_D = 0.059$ (36.9% below Grid Search), and improves RL return by 50% over Grid Search. All advantages over non-ALMAB baselines are statistically significant under Bonferroni-corrected Mann--Whitney $U$ tests. Distributed execution achieves $7.5\times$ speedup at $K = 16$ agents, consistent with Amdahl's Law.

For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a popular tool to discover these missing physics. Universal differential equations employ neural networks to represent missing parts of the model structure, and symbolic regression aims to make these neural networks interpretable. These machine learning techniques require high-quality data to successfully recover the true model structure. To gather such informative data, a sequential experimental design technique is developed which is based on optimally discriminating between the plausible model structures suggested by symbolic regression. This technique is then applied to discovering the missing physics of a bioreactor.

It is increasingly important to evaluate the characteristics of systems based on large language models (LLMs). Evaluations in this context often rely on a curated benchmark set of input prompts provided to the LLM, where the output for each prompt may be assigned a binary or ordinal score and the aggregation of scores across prompts is then used as a summary evaluation. In this paper, we develop a Bayesian approach for quantifying the uncertainty that arises in such evaluation metrics as a result of the stochasticity of the LLM-based systems; the same prompt may exhibit different outcomes on repeated runs. Our framework leads naturally to a sequential evaluation, in which we leverage the Bayesian model to preferentially select which prompts in the benchmark to use next, enabling more cost-effective LLM evaluations. We demonstrate this approach through four case studies: pairwise LLM preferences in interactive dialogue (MT-Bench), refusal rates on adversarial inputs (JailbreakBench), embodied agentic reasoning (ALFWorld), and agentic web-search Q&A (GAIA). Our results illustrate how a Bayesian approach can provide insightful uncertainty quantification about the behavior of blackbox LLM-based systems in a manner that is not accessible via deterministic or single-run evaluations.